A ceremony was held yesterday after the stone was moved further up the Water of Leith from near Forsyth Barr Stadium to the steps on the western bank opposite the University of Otago's clocktower.
The stone, which was installed in 2011, was planned as part of a sculpture walk that never eventuated.
The move was prompted by a request from the Dunedin-Edinburgh Sister City Society, which worked with the university to select a site.
Dunedin City Council group manager arts and culture Bernie Hawke said at the ceremony that the new location was perfect, given the university's Scottish heritage.
The stone cost the council about $20,000 to move, which included the cost of a new plinth and the heavy machinery required, Mr Hawke said.
``It's not something you would lift up and put in your back pocket.''
Dunedin-Edinburgh Sister City Society chairman Bruce Nicholson said it was thrilled with the new location.
University property services division director Barry MacKay was also delighted.
``The university is pleased to have the opportunity to provide a new home for this commemorative stone, particularly because we have such strong links to Scotland,'' Mr MacKay said.
Members of the Free Church of Scotland Thomas Burns and James Macandrew lobbied for the endowment of land for the university, which followed the Scottish model when it was founded in 1869.
The Edinburgh Stone's distinctive shape was formed from Aberdeenshire granite by Sylvia Stewart in 2007.
A sister piece named Owheo, made from a rock lifted from the Water of Leith in 1999, sits on the Edinburgh waterfront. An earlier-presented stone from Edinburgh is installed on Signal Hill near Dunedin's Centennial Memorial.